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 Nov 28 comment Adding two random variables (probability distributions) Just as a tiny comment: it would be better to first evaluate: ee = PDF[tf, x], and then DiscretePlot[ee {x, 2, 12}] . By contrast, DiscretePlot[PDF[tf, x], {x, 2, 12}] might take about 100 times longer to plot, because it tells Mma to calculate PDF[t,x] at each value of x (rather than just solving it once). Nov 8 comment How to model rolling a pair of dice 100 times (Monte Carlo) What is the relevance of the 100 times? Are you seeking a sampling distribution of some statistic that depends on the sample size? Oct 24 comment More efficient method to compute moments of the Johnson $S_B$ distribution Could you please provide your favorite reference for Pearson fitting functions?  .... Recent versions of Mma have some in-built Pearson functions. Chapter 5 of our book has extensive coverage of doing Pearson fitting w ... you can download a free copy of the chapter here: mathstatica.com/book/bookcontents.html Oct 24 comment More efficient method to compute moments of the Johnson $S_B$ distribution As you have noted, the moments of the Johnson $S_B$ system are extremely complicated. As such, the method of moments is not generally used for fitting $S_B$ systems. Instead, a method of percentile points is usually used, which equates percentile points of the observed and fitted curves. The latter is not an exact methodology. I have come across some new alternative fitting methods in recent years. One can also always use Pearson fitting functions as a substitute, which is inevitably a much simpler strategy. Oct 2 comment Mathematica function to calculate equivalent NormalDistribution from a WeibullDistribution The diagram illustrates neatly that the two distributions are not equivalent ... and thus too that the OP's first question should be dropped or modified, because there is NO equivalent Normal distribution. David's answer above addresses the OP's second question very nicely. However, perhaps the OP should ponder why he is only making use of the first 2 (sample?) moments as the basis to fit his Weibull pdf ... and ignoring higher moments that may readily be available. Oct 2 comment Mathematica function to calculate equivalent NormalDistribution from a WeibullDistribution I have also downvoted this, because the first question is confusing and has no proper answer. The second question is perfectly respectable. Oct 2 revised A tricky algebraic simplification added 95 characters in body Oct 2 comment A tricky algebraic simplification I think you are missing the point: you do not need the x's. Chuck in a number like 0 and it works fine [see my revised answer below ] ... same for the $n = 4$ case. Does this mean you are going to change the question again ... :) Oct 2 revised A tricky algebraic simplification added 582 characters in body Oct 2 comment A tricky algebraic simplification You keep on changing the question. Also, your solution ans = f[x]/gau[x - mn, v] does not make sense .... Do you perhaps intend that v to be vn? Oct 2 revised A tricky algebraic simplification added 168 characters in body Oct 2 revised A tricky algebraic simplification added 63 characters in body Oct 2 revised A tricky algebraic simplification added 63 characters in body Oct 2 answered A tricky algebraic simplification Oct 1 comment Mathematica function to calculate equivalent NormalDistribution from a WeibullDistribution There is no equivalent Normal distribution to match your Weibull distribution. For starters, the Weibull has a strictly positive domain of support and is skewed, whereas the Normal is defined on the real line and is symmetrical. Sep 7 comment How to sustain (pedal) a note? If the question is to sustain (pedal) 'a note' ... as in a single note ... what would be the difference between holding the pedal vs increasing the duration of the note? With multiple notes held (and new ones being played on top), things get more interesting with harmonics and such ... This may be even the case with a single note being played (since ALL the strings are not damped while the pedal is pressed ... so they all resonate) ... but it does not seem to me that you are asking a question about the subtleties of harmonics?? Or are you? Sep 7 comment Selecting numbers from a list Could you please clarify what you mean by "pair of numbers which differ by 2". Given a list {1,2,4,7,6,8,9}, do you seek the output: {{2,4}, {6,8}}, or the output {{2,4}, {4,6}, {6,8}, {7,9}} ?? I would have thought that your terminology 'pair' suggested the former, but perhaps you seek the latter. Sep 6 comment Calculate the mean of ordered distribution of the defined distribution Re Edit ---> much improved!! This is, I think, in itself a beautiful illustration of the advantage of openness and friendly interaction with others. All the better for the ability to compare different output and different ways of working, which is what this site is all about. Sep 6 comment Calculate the mean of ordered distribution of the defined distribution Well, it seems you have a bone to pick with a large number of Wolfram staff members here. Sep 5 revised Calculate the mean of ordered distribution of the defined distribution added 504 characters in body